The Level Two and Three Modular Invariants of SU (n)

In this Letter, we explicitly classify all modular invariant partition functions for at levels 2 and 3. Previously, these were known only for level 1. Level 2 exceptions exist at r=9, 15, and 27;level 3 exceptions exist at r=4, 8, and 20. One of these is new, but the others were all anticipated by the rank-level duality relating level k and level r+1. The main recent result which this Letter rests on is the classification of -type invariants.